Solving Fracture Mechanics Problems By The Meshless Intervention-point Method And Its Engineering Applications

The meshless method is a new numerical method in solving partial differential equations,whose most outstanding advantage is thoroughly or partly eliminates meshing and becoming easy to solve high velocity impact problems,blasting problems,super-large deformation problems and crack propagation problems et al.The meshless intervention-point(MIP)method is a collocation meshless method,it uses the moving least squares kernel approximation(MLSc),the moving least squares derivative approximation,intervention-point principle and local intervention-point approximation et al.to get better stability and higher precision than the normal meshless collocation methods.On the basis of the theory of the MIP method and its applications,applications of the MIP method to linear-elastic fracture mechanics problems are presented in this thesis.At the beginning of the thesis,the MIP method is introduced from some aspects of the moving least squares kernel approximation,the moving least squares derivative approximation,intervention-point principle and local intervention-point approximation et al.Two numerical problems are presented to demonstrate the feasibility of the MIP method,results show that the MIP method is validity in solving normal linear-elastic problems and singular problemsIn this thesis,the modified MIP method is used to investigate several kinds of linear-elastic fracture mechanics problems.The MIP method is modified to adapt the stress-singularity in the linear-elasctic fracture mechanics problem with the enriched basis function and a visibility criterion,a detail algorithm is proposed for the visibility criterion to solve non-continuity of cracks;Three methods for solving stress intensity factor are introduced,i.e.J integral,stress-based extrapolation method and displacement-based extrapolation method;The stress field and the stress intensity factor et al.are given for several kinds of cracked plates,the validity of the mode ? and mode ? stress intensity factor coefficients observed by the MIP method and the meshless collocation method for different crack states are analyzed;For the analysis of quasi-static crack propagation,a rectangular central oblique cracked plate under uniformly uniaxially stretch is simulated,the stress intensity factor coefficients and their effects are analyzed between crack propagations;The cracked retaining wall is simulated by the MIP method,the displacements and stresses field between different crack growth processes are obtained,it is of an important significance for the protection and reinforcement for the retaining wall.Numerical results show that the present method possesses not only feasibility and validity,but also high accuracy and good performance of convengence for linear-elastic fracture mechanics problems.In addition,the method of particular solution(MPS)and the method of least square series(MLSS)are presented in solving fourth-order partial differential equations,the advantages and disadvantages are analyzed by four numerical examples,results show that the number of nodes in problem domain and the order of the polynomial basis are the most important factors for the accuracy and stability.